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; HW03.lisp - Homework Assignment #3 for CS408, Fall Quarter, 2006
; Copyright (c) 2006 Ira W. Snyder (devel@irasnyder.com)
;
; Permission is hereby granted, free of charge, to any person obtaining a copy
; of this software and associated documentation files (the "Software"), to deal
; in the Software without restriction, including without limitation the rights
; to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
; copies of the Software, and to permit persons to whom the Software is
; furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in all
; copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
; OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
; SOFTWARE.

;;; Problem 1
(defun PALINDROME (LI)
  (append LI (reverse LI))
)

;;; Problem 2
(defun PALINDROMEP (LI)
  ; define a local function so we can do this tail-recursively
  (labels ((PAL-HELP (L1 L2)
              (cond
                ((null L1)                 t)
                ((equal (car L1) (car L2)) (PAL-HELP (cdr L1) (cdr L2)))
                (t                         nil)
              )
            ))
    ; call the tail-recursive local function
    (PAL-HELP LI (reverse LI))
  )
)

;;; Problem 3
(defun DIVISIBLE-BY-N (DIVIDEND DIVISOR)
  (cond
    ((= (mod DIVIDEND DIVISOR) 0) t)
    (t                            nil)
  )
)

;;; Problem 4
(defun SQUASH (LI)
  (cond
    ((null LI) nil)
    ((atom LI) (list LI))
    (t         (append (SQUASH (car LI)) (SQUASH (cdr LI))))
  )
)

;;; Problem 5
(defun COUNT-ATOMS (LI)
  (cond
    ((null LI) 0)
    ((atom LI) 1)
    (t         (+ (COUNT-ATOMS (car LI)) (COUNT-ATOMS (cdr LI))))
  )
)

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